What search engine means
The name describes what the system does: it searches by itself. There is no central registry of the web. The search engine discovers pages on its own by following links and reading sitemaps, and it decides which pages to store and in what order to show them.
A search engine is different from a web directory, where people sort websites by hand, and from an AI assistant that writes an answer. The lines are blurring, though: Google shows AI-generated overviews above its results, and several AI assistants query a search index before they answer.